#estimates and converges on e=2.718..
def est_e(limit = 20):
  x = 1.391925581569705
  _f = 596.25 #596.25
  _e = (((1/(((((1/log(x, pi-0.5))-1))-1)*(x-1)))-(1/((((1/_f)*17)+17)**2))))
  i = 0
  while i < limit:
    v = log(1/(log(_e)-1))
    _e = ((((1/(((((1/log(x, pi-0.5))-1))-1)*(x-1)))-(1/((((1/_f)*17)+17)**2)))) - (1/(_e**v)))
    _f = 1/((((1/((1/(((((1/log(x, pi-0.5))-1))-1)*(x-1)))-_e))**0.5)/17)-1)
    i = i + 1

  print("done!")
  print(f"estimate e: {_e},  actual: {e},  ratio: {_e/e}")
  return _e, e